three-period crossover trial with ambulatory blood pressure monitoring for evaluating...

Three-period crossover trial with ambulatory blood pressure monitoring for evaluating antihypertensive therapy

Suzanne Meeves, PharmD, MBA, Kerry Hafner, PhD, Glen Park, PharmD, and Michael Weber, MD Kansas City, Mo., and Long Beach, Calif.

A double-blind, three-period, crossover trial used 24-hour ambulatory blood pressure monitoring to compare diltiazem controlled diffusion (CD) 300 mg with placebo. Patients with hypertension (N = 43) were randomly assigned to one of four crossover treatment sequences of three treatment periods each. Ambulatory blood pressure was obtained at the end of each 4-week treatment period. Diltiazem CD significantly decreased diastolic and systolic blood pressure at bihourly ambulatory blood pressure evaluations (p < 0.05, all). How- ever, when all ambulatory blood pressure monitoring data were combined into one statistical model, blood pressure reductions were quantifiably similar to those in the overall bihourly analysis, but with a consistent 24-hour antihypertensive effect for both diastolic and systolic blood pressure relative to that with placebo (i.e., parallel blood pressure profiles) and with increased precision. Mean _ SE changes in diastolic and systolic blood pressure across the 24-hour dosing interval were -5.6 _ 0.4 mm Hg and -7.6 _ 0.5 mm Hg, respectively (p< 0.001, both). Therefore, by using a crossover design with ambulatory blood pressure monitoring, we showed diltiazem CD to reduce blood pressure consistently throughout a 24-hour dosing interval in comparison with placebo in patients with hypertension. (AM HEART J 1995;130:841-8.)

Ambulatory blood pressure monitoring (ABPM) is used to record and evaluate patients' blood pressure at set intervals over a specific time period (e.g., every hour for 24 hours). It has several applications in both clinical practice and research settings. 1 In clinical practice, ABPM may provide the additional information needed to make difficult diagnostic and ther- apeutic decisions. For example, ABPM may be more indicative of end organ damage than are conven-

From Marion Merrell Dow Inc., Kansas City, and the Veterans Adminis- tration Medical Center, Hypertension Center, Long Beach.

Supported by grants from Marion Merrell Dow Inc.

Received for publication Feb. 27, 1995; accepted April 5, 1995.

Reprint requests: Suzanne G. Meeves, PharmD, MBA, Marion Merrell Dow Inc., P.O. Box 9627, Kansas City, MO 64134-0627. 4/1/65568

tional blood pressure measurements by sphygmomanometer. The development of left ventricular hypertrophy, and probably renal dysfunction and ret- inopathy as well, is more highly correlated with elevations in blood pressure obtained by ABPM than by sphygmomanometer. 2-7 ABPM also has utility in screening patients who truly have hypertension as opposed to those who demonstrate "white-coat hypertension. ''8-10

In pharmaceutical development, ABPM can be used to characterize a drug effect on blood pressure over time, including establishing time to onset, time of peak effect, and duration of action. Another attractive feature of ABPM is the improved precision of the estimated antihypertensive effect with repeated measures of blood pressure, thereby reducing the sample size required for clinical drug evalua- t i o n . 11, 12 Variance is reduced because repeated blood pressure measurements are obtained from the same patient and because ABPM produces little or no placebo effect. 13-15

Variability can also be decreased by using certain study designs that were developed for that purpose. The crossover (or changeover) trial is a popular study design in which each patient receives all treatments. The primary advantage of the crossover design, as compared with the parallel group design, is that t reatments can be compared within an individual patient, as opposed to across groups of patients, thus leading to variance reduction. As such, fewer patients are required for demonstration of efficacy. Crossover designs are most appropriate for situa- tions in which the patients' condition returns to baseline levels after a sufficient duration of treatment withdrawal or transition. Moreover, some ex- tended-period (i.e., more than two periods) crossover designs enable the estimation of the t reatment effect independently of the "carryover effect," even if the carryover effect is significant. 16"1s This point has generated considerable debate about the validity of

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the (two-period) crossover trial. Our purpose is to describe a three-period, two- t rea tment crossover tr ial in which 24-hour ABPM was used to compare the an t ihyper tens ive effects of a once-daily formula- t ion of di l t iazem (Cardizem CD) wi th those of a placebo. Par t i cu la r emphas is is given to the efficiencies t ha t are gained from the crossover trial design and ABPM.

METHODS Study design. This study was a multicenter, random-

ized, double-blind, three-period, two-treatment crossover trial designed to compare diltiazem CD 300 mg with placebo. The trial was divided into two segments: an initial single-blind 2- to 3-week placebo baseline segment and a 12-week treatment segment divided into three 4-week periods (Fig. 1). Previous experience with diltiazem sug- gested that 4 weeks of treatment before ABPM was sufficient to assume that the effect on blood pressure from any previous treatment (i.e., the carryover effect) would be negligible. Therefore, washout periods were not incorpo- rated between adjacent treatment periods.

After the discontinuation of all antihypertensive medications for at least 2 weeks, patients entered the placebo baseline segment. Ambulatory patients who had moderate essential hypertension (100 mm Hg <-supine diastolic blood pressure (DBP) -< 110 mm Hg) and were 18 to 65 years of age were considered for entry into the trial. Patients with significant renal, hepatic, neurologic, endo- crine, or cardiovascular disease other than hypertension were excluded from study participation. Premenopausal women of childbearing potential or patients requiring medications known to affect blood pressure were also excluded from study participation.

Eligible patients were randomly assigned to receive one of the following four treatment sequences: (diltiazem -~ placebo --) diltiazem), (diltiazem --> placebo --) placebo), (placebo --~ diltiazem --> diltiazem), or (placebo --> diltiazem --> placebo). The other four possible treatment sequences, (diltiazem --> diltiazem ---> placebo), (placebo ---> placebo --->

diltiazem), (diltiazem -~ diltiazem ~ diltiazem), and (placebo--) placebo--) placebo), were excluded from this trial because the (diltiazem ---> diltiazem ---) diltiazem) and (placebo -~ placebo ~ placebo) sequences do not contribute to the within-patient estimation of treatment effect, and none of the four treatment sequences contribute to the within-patient estimation of treatment carryover effect. 16 The blinded treatments were administered as 180 mg/day for the first week and then increased to 300 rag/day for the remaining 3 weeks of each treatment period. Blood pressure responses to treatment during the dosing interval were measured by 24-hour ABPM at the end of each 4-week treatment period.

The protocol for this study was approved by an Institu- tional Review Board at each study site. All patients gave written informed consent before enrollment into the study.

Study evaluations. Supine blood pressure measurements taken during routine and qualification visits were obtained in triplicate at trough (i.e., at 8 AM _+ 1 hour and at 24 +- 2 hours after the dose). These measurements were obtained by trained clinical study personnel with a stan- dard mercury sphygmomanometer using phases i and 5 of the Korotkoff sounds as the indicators of systolic blood pressure (SBP) and DBP, respectively.

The 24-hour ABPM sessions conducted at end-weeks 4, 8, and 12 were initiated with the patient in a fasting state at 8 AM -+ 1 hour and 24 _+ 2 hours after the dose. The end- week 8 and end-week 12 ABPMs were both initiated within I hour of the clock time of the end-week 4 ABPM initiation. The SpaceLabs model 90207 monitor (SpaceLabs Inc., Redmond, Wash.) was used for ABPM, with the monitor validated against simultaneous cuff measurements. Infla- tion intervals were programmed randomly four times per hour from 0600 to 2159 military time, and twice per hour from 2200 to 0559. The resulting ABPM measurements were edited, and outlier data (SBP <70 or >260 mm Hg; DBP <40 or > 150 mm Hg; heart rate <20 or >200 beats/min) were deleted. In addition, each ABPM value was compared with the mean value of the three preceding and three following readings and deleted if the value differed from the mean of the six surrounding readings by >30% and >2 SD.

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The 24-hour monitoring procedure was considered successful if->69% of the readings were successful.

Medication compliance was assessed by capsule count, with acceptable limits for qualification in the range of 70% to 130%. Safety evaluations included heart rate measurements at each study visit, 12-lead electrocardiograms, fasting laboratory measurements at baseline and end of study, and adverse event monitoring throughout the trial.

Statistics. In this three-period, two-treatment crossover trial, each protocol-compliant patient received both diltiazem CD and placebo. For this reason, comparisons between the two treatments could be made within each patient, rather than between groups of patients. Fewer patients were required to evaluate efficacy with this trial design because the variability within a patient is typically less than the variability between groups of patients. 161s The sample size for this study was estimated so that ade- quate power would be provided to detect an average treatment difference of 5 mm Hg. On the basis of a two-sided,

= 0.05 level t test and a within-patient SD of 8 mm Hg, it was determined that a minimum of 40 protocol-compliant patients would be required to achieve at least 80% statistical power. 19

The primary goal of the statistical analysis was to compare the blood pressure-lowering effects of diltiazem CD with those of placebo throughout the 24-hour dosing interval. For this purpose, bihourly means were computed for each patient at each end-period ABPM evaluation. The 12 bihourly means were computed by averaging the available blood pressures in each 2-hour interval: hour 1 was used to designate the time interval 8:00 A~ to 9:59 AM, hour 3 for 10:00 AM to 11:59 AM, etc. An overall mean, defined as the average of the 12 bihourly means, was also computed for each patient and was used to provide a single summary measure of the treatment effect across the 24-hour dosing interval. As stated in the clinical protocol, DBP was the primary response variable, and SBP and heart rate were of secondary interest. Patients judged before unblinding to have maj or protocol deviations (e.g., ingestion of prohibited medications) were excluded from all efficacy analyses in accordance with the clinical protocol.

Two types of linear mixed-effects models were used to compare the two treatments. First, 12 separate mixed- model analyses of variance were used to assess treatment and carryover effects for each of the 12 bihourly means. These mixed models contained DBP (or SBP, heart rate) as the response variable, with investigative site, t reatment sequence, treatment, period, and first-order carryover as fixed factors and patient and experimental error as random factors. The same type of mode] was used to analyze the subjects' overall mean responses (i.e., the average of the 12 bihouriy means).

A second type of mixed model included all 12 bihourly means for DBP (or SBP, heart rate) into one analysis. The 24-hour profiles of each treatment were modeled by use of orthogonal polynomials, both in the fixed effects and in the subject-specific random effects. The fLxed-effects compo- nent of the model included terms for investigative site, t reatment sequence, treatment, period, and first-order

carryover. The random effects included experimental error terms and subject-specific orthogonal polynomial coefficients that were used to model diurnal variation. These random subject-specific polynomial coefficients represent a subject's random diurnal deviation about the population (fLxed-effect) curve. A backward elimination procedure was used to develop an appropriate statistical model.

The first type of mixed model mentioned above is useful for comparing the treatments at specific time intervals (e.g., comparing the beginning with the end of the dosing interval). The second type of mixed model consolidates all of the blood pressure data into one model and, unlike the analyses of the 12 separate mixed models, allows the consistency of the treatment differences to be compared statistically. In both mixed models, investigator and sequence assessments were based on between-patient variability, whereas treatment, period, and carryover assessments were based on within-patient variability. All statistical analyses were conducted by using SAS statistical soft- ware. 20

RESULTS Patient sample. Sixty-five pa t i en t s were screened

for s tudy par t ic ipa t ion a t five inves t iga t ive sites. Fif ty-one of those pa t i en t s were r a n d o m l y ass igned to one of the four t r e a t m e n t sequences and received the s tudy drug. O£ those 51 r andomly ass igned pa t ien ts , 8 were considered (before unbl inding) to have major protocol violations: 6 p r e m a t u r e l y dis- cont inued s tudy par t ic ipa t ion and 2 h a d i nadequa t e ABPM for analysis . The r e m a i n i n g 43 protocol-com- p l ian t pa t i en t s were included in all p r i m a r y and sec- onda ry s ta t i s t ica l analyses .

Base l ine and demograph ic in format ion for the 43 protocol-compliant pa t i en t s a re d isplayed in Table I. All pa t i en t charac ter i s t ics were s imi lar a m o n g the four t r e a t m e n t sequences, wi th the possible excep- t ions of race, weight , and base l ine h e a r t rate . These a p p a r e n t differences, however , were not s ta t i s t ica l ly s ignif icant (all p va lues >0.15). Pa t i en t s serve as the i r own controls in crossover t r ials , and hence demograph ic imba lances a m o n g the t r e a t m e n t sequences a re typical ly of no consequence.

Efficacy results. Dil t i azem CD was effective in lower ing DBP th roughou t the 24-hour dosing interval . The s epa ra t e mixed-model ana lyses of the ABPM d a t a a t each o f the 12 b ihour ly in te rva ls indicated t h a t d i l t i azem CD lowered DBP signif icant ly more t h a n placebo t h roughou t the 24:hour dosing in te rva l ( a l lp va lues < 0.05; Table II). The major i ty of the bi- hour ly m e a n res idua l effects, defined as the dilt- i a zem CD m e a n D B P minus the placebo m e a n DBP, were s imilar . The l a rges t m e a n res idua l effect, -8 .4 m m Hg, occurred a t the end of the 24-hour dosing interval . The overall m e a n _+ SE res idual effect across the 24-hour dosing in te rva l was -5 .4 _+ 0.8

844 Meeves et al.

Table I. Summary of demographic information for all protocol-compliant patients

October 1995 American Heart Journal

D-->P ~ D D ~ P - ~ P P ~D-->D P ~ D ~ P Total Patients (n = 12) (N = 11) (N = 11) (N = 9) (N = 43)

Sex M (n) 7 7 8 5 27 F (n) 5 4 3 4 16

Race Whi t e (n) 4 6 8 6 24 Nonwhi t e (n) 8 5 3 3 19

Age (yr) 52 _+ 11" 52 _+ 12 55 +- 8 50 +_ 11 52 _+ 11 He igh t (in) 67 _+ 4 68 _+ 5 67 ___ 4 68 -+ 5 68 _+ 4 W e i g h t (lb) 187 _+ 29 201 +_ 50 190 _+ 35 200 -- 42 194 _+ 38 DBP (ram Hg) 102 + 2 103 _+ 2 103 _+ 2 104 _+ 2 103 +_ 2 SBP ( m m Hg) 155 -+ 13 158 +_ 16 157 _+ 8 159 _+ 15 157 _+ 13 H R (beats /min) 74 _+ 8 67 _+ 6 71 -+ 7 74 -+ 10 71 +_ 8

D, Diltiazem; P, placebo; HR, heart rate. *Values are expressed as mean + SD.

Table ]]. Summary of DBP at each bihourly evaluation of the 24-hour ABPM session

Diltiazem CD Placebo Residual effect p Value Hour (mean) (mean) (mean +- SE) (diltiazem vs placebo) 95% Confidence interval

1 97.2 103.7 -6 .5 -+ 1.4 <0.001 (-9.2, -3 .9) 3 93.9 98.9 -5 .0 +- 1.3 <0.001 (-7.6, -2.4) 5 91.8 ' 97.9 -6 .1 -+ 1.6 <0.001 (-9.2, -2 .9) 7 91.4 96.8 -5 .4 +- 1.3 <0.001 (-8.1, -2.8) 9 92.7 97.3 -4 .6 -+ 1.3 <0.001 (-7.1, -2 .1)

11 92.6 96.2 -3 .6 -+ 1.3 0.006 (-6.1, -1 .1) 13 86.7 92.5 -5 .8 -+ 1.5 <0.001 (-8.8, -2 .8) 15 83.1 88.2 -5 .1 -+ 1.7 0.003 (-8.4, -1 .8) 17 82.1 85.3 -3 .2 -+ 1.4 0.023 (-5.9, -0.5) 19 81.3 86.4 -5 .1 -+ 1.5 0.001 (-8.1, -2 .1) 21 86.4 92.3 -5 .9 +- 1.4 <0.001 (-8.6, -3 .1) 23 92.5 100.9 -8 .4 -+ 1.2 <0.001 (-10.7, -6.1)

Overa l l 89.1 94.5 -5 .4 + 0.8 <0.001 (-7.0, -3 .8)

DBP values are given in millimeters of mercury.

mm Hg (p < 0.001). The carryover effect from one period to the next was found to be negligible in all 12 analyses.

The second type of mixed model was used to compare statistically the consistency of the t rea tment differences across the 24-hour dosing interval. The results from that analysis indicated that the 12 mean residual effects were not statistically different from one another, or equivalently tha t the 24-hour DBP profiles for diltiazem CD and placebo were parallel. The common mean +- SE residual effect was estimated to be -5.6 +- 0.4 mm Hg (p < 0.001). The mag- nitude of this t rea tment difference concurs with that of the former overall mean analysis, although a 100% reduction in variability (SE = 0.4 vs 0.8 mm Hg) was achieved by incorporating all of the DBP data into a single analysis. The smoothed parallel curves obtained from this analysis are displayed in Fig. 2 to depict the diurnal variation with consistent residual

effect (i.e., the vertical distance between the two curves is 5.6 mm Hg at all time points). The results for SBP were similar to those for DBP. In particular, separate analyses of the ABPM data at bihourly intervals indicated that diltiazem CD lowered SBP significantly more than placebo at all 12 bihourly evaluations (allp values < 0.05; Table III) and overall (p < 0.001). The mean residual effects ranged from -5.3 to -9.7 mm Hg, with an overall mean -+ SE residual effect across the 24-hour dosing interval of -7.6 _+ 1.3 mm Hg. As with DBP, the mean residual effects were found to be consistent throughout the 24-hour dosing interval (Fig. 3). The common mean _+ SE residual effect was estimated from the second type of mixed model to be -7.6 + 0.5 mm Hg (p < 0.001). A greater than 100% reduction in variability was again achieved by including all of the data into a single analysis.

Diltiazem CD also tended to lower hear t rate dur-

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Fig. 3. Estimated mean (_+1 SE) SBP during 24-hour dosing interval.

Table III. Summary of SBP at each bihourly evaluation of the 24-hour ABPM session

Diltiazem CD Placebo Residual effect p Value Hour (mean) (mean) (mean +_ SE) (diltiazem vs placebo) 95% Confidence interval

1 150.2 159.6 -9.4 -+ 1.7 <0.001 (-12.8, -6.0) 3 147.7 156.0 -8.3 +- 2.0 <0.001 (-12.2, -4.4) 5 145.7 154.3 -8.5 -+ 1.8 <0.001 (-12.0, -5.1) 7 143.8 153.5 -9.7 -+ 1.8 <0.001 (-13.3, -6.1) 9 147.2 153.6 -6.4 + 1.7 <0.001 (-9.8, -3.0)

11 147.8 154.0 -6.1 -+ 1.7 <0.001 (-9.4, -2.8) 13 143.5 150.1 -6.6 -+ 2.0 0.001 (-10.5, -2.8) 15 136.8 144.5 -7.7 _+ 2.1 <0.001 (-11.8, -3.5) 17 135.6 140.9 -5.3 -+ 2.1 0.015 (-9.4, -1.1) 19 133.3 140.4 -7.0 -+ 2.1 0.001 (-11.2, -2.9) 21 139.3 145.4 -6.2 -+ 2.2 0.007 (-10.5, -1.8) 23 145.5 154.9 -9.5 + 1.8 <0.001 (-13.1, -5.9)

Overall 143.3 150.9 -7.6 _+ 1.3 <0.001 (-10.1, -5.1)

SBP values are given in millimeters of mercury.

ing the 24-hour dosing interval. Analys is of the data at bihourly intervals indicated that di l t iazem CD lowered heart rate s ignif icantly more than placebo at 8 of the 12 evaluat ions (p < 0.05; Table IV). The overall mean _ SE residual effect was -2 .7 _+ 0.7 beats/m{n (p < 0.001). The mean residual effects for heart rate were also found to be consis tent across the 24-hour dos ing interval (Fig. 4). The common mean _+ SE residual effect for heart rate was est imated from the second type of mixed model to be -3 .2 _+ 0.5 beats/mAn (p < 0.001). The magni tude of this treat-

ment difference, however, suggests that the heart rate reductions from diltiazem CD were typically modest.

Safety results. Of the 51 randomly assigned patients, 47 received at least one dose of diltiazem CD and 50 received at least one dose of placebo. The per- centage of patients having adverse events that were assessed by the investigator as resulting from study medication was 14.9% (7/47 patients) for diltiazem CD and 10% (5/50 patients) for placebo. No serious treatment-related events occurred during the trial.

October 1995 846 Meeves et al. American Heart Journal

Table IV. Summary of heart rate at each bihourly evaluation of the 24-hour ABPM session

Diltiazem CD Placebo Residual effect p Value Hour (mean) (mean) (mean ± SE) (diltiazem vs placebo) 95% Confidence interval

1 79.1 81.4 -2.3 _+ 1.2 0.070 3 83.0 83.0 0.0 _+ 1.7 0.984 5 81.2 83.8 -2.6 +_ 1.4 0.072 7 79.3 84.0 -4.7 _+ 1.3 <0,001 9 79.6 83.2 -3.6 ± 1.3 0,005

11 79.6 82.3 -2.7 ± 1.3 0.042 13 76.4 79.0 -2.6 ± 1.2 0.036 15 72.6 75.0 -2 .5 _+ 1.1 0.031 17 69.6 72.9 -3.3 _+ 1.0 0.002 19 68.5 71.1 -2.6 ± 1.0 0.011 21 71.0 73.8 -2.8 _+ 1.3 0.029 23 79.1 81.4 -2.3 _+ 1.3 0.076

Overall 76.3 79.0 -2.7 _+ 0.7 <0.001

(-4.7, 0.2) (-3.4, 3.4) (-5.5, 0.2)

(-7.3, -2.1) (-6.1, -1.1) (-5.3, 50.1) (-4.9, -0.2) (-4.7, -O.3) (-5.3, -1.3) (-4.5, -o.6) (-5.3, -0.3) (-4.8, 0.2) (-4.1, -1.2)

Heart rate values are given in beats per minute.

DISCUSSION

In this clinical trial, diltiazem CD produced a smooth, consistent blood pressure-lowering effect throughout a 24-hour dosing interval. We showed this blood pressure-lowering effect in a trial that in- corporated several study design features to maxi- mize the assessment of a t reatment response: (1) we included patients with office DBPs of at least 100 mm Hg to reduce the likelihood of inclusion of patients with white-coat hypertension; (2) we used 24-hour ABPM to reduce variability in the blood pressure assessments; (3) we used a statistical model that incorporates all of the data into a single analysis, yet retains the diurnal pattern, to improve the precision of the estimated t reatment differences; and (4) we used a three-period, two- t reatment crossover trial so that t reatments could be compared within patients to reduce response variability. For the comparison of two treatments, the variance of this three-period crossover design is 3/32 of tha t for a two-period crossover design trial.

A goal of pharmaceutical development for antihypertensive compounds is to show the blood pressure- -lowering effects of the compound in a precise, cost- effective, yet clinically relevant manner. Traditional antihypertensive drug development focuses on measurement of s tandard clinic cuffblood pressure measurements. However, over the last several years ABPM has gained increased attention as a method to evaluate antihypertensive therapy with increased precision, cost-effectiveness, and clinical relevance. 1

ABPM has been used to increase the precision of blood pressure response by virtue of the larger number of measurements taken. The larger number of measurements reduces the variability associated

with biologic fluctuations such as those related to patient activity and the variability associated with random instrument and operator errors in cuffblood pressure measurement. 11-14

However, uncertainty has existed about how best to analyze the data, with researchers split into three main schools of thought. 1, 21, 22 One school of thought is that the best method is to conduct a simple analysis of some measure of central tendency of blood pressure over the entire time of measurement or over periodic intervals, such as hourly or bihourly intervals or night and day intervals, s, 23, 24 The main lim- itation of this method is that it treats each time interval as being independent, thus ignoring the con- tribution of the adjacent time interval(s). A second school of thought is that the best method is to reduce the data to a categoric analysis of responder versus nonresponder. A "responder" might be defined as a patient who has a predefined percent reduction in "abnormal" blood pressure measurements, s, 25 This method is useful for assessing response in an individual patient but may lack statistical power for showing t reatment response; also, the definitions of responder and abnormal blood pressure are some- what arbitrary. Another school of thought is that the best method is to use data-smoothing techniques such as Fourier transformation, spline functions, or the cosinor method to make use of all of the data col- lected in the analysis and describe the normal diurnal blood pressure variation. 26-28 These methods are generally complicated and do not lend themselves easily to accurate statistical testing, such as for

1 21 22 comparing t rea tments . , , In this trial, two different statistical models were

used in the analysis of the ABPM data. One of these

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models evaluated the 12 bihourly means individu- ally and overall; the other model combined all 12 bihourly means into one analysis. By evaluating the 12 bihourly means separately, specific time intervals of blood pressure reduction could be compared without a great concern of oversmoothing. One drawback to this analysis is that each bihourly measurement is considered separately and hence does not contribute to estimation and inference of adjacent time points. Moreover, this analysis is plagued by the "multiple t test" problem; that is, p values should be adjusted for the multiplicity of tests that are done. Of note, most of the bihourly mean residual effects for DBP and SBP were similar, and the overall mean residual effects for DBP and SBP from this model agreed with the overall mean residual effects estimated from the second model.

The advantage of the second model is that it provides a statistical comparison of the consistency of the t reatment effects for diltiazem CD versus placebo; that is, it provides for a test of parallel curves. In addition, this second model generates smoothed blood pressure curves without data transformation. As expected with the combination of the bihourly DBP or SBP data in one analysis, the precision of the estimated t reatment differences was greatly improved. By improving the precision of the estimated t reatment effect, the number of patients required to

show a clinically important t reatment effect is dra- matically reduced. In a comparison of the two analysis methods used in this study, the second model approximately doubled the precision of the estimate of the t reatment effect. Thus, the cost-effectiveness of clinical trials can be increased considerably. To our knowledge, this method of analysis has not been previously applied to ABPM data.

Finally, the study design and analysis model were useful to show that diltiazem CD lowered blood pressure consistently over the 24-hour dosing interval, producing a blood pressure curve parallel to that of placebo. This consistent t reatment effect is clinically important, inasmuch as the shape of the 24- hour blood pressure curve may be an important prognostic factor. It is assumed that treatments that reduce the morbidity and mortality of hypertension lower blood pressure consistently throughout the day, particularly during the early morning hours when the risk of myocardial infarction is highest. In contrast are data that suggest that treated hyper- tensive patients who achieve excessive blood pressure reductions have a higher incidence of cardiovascular events.29, 30 Thus, consistent blood pressure control, as was shown with diltiazem CD in this study, may be an important goal of antihypertensive therapy.

We thank Joan M. Grebin, BS, MBA, for assisting in the man- agement of this clinical trial, and Professor Ronald W. Helms, University of North Carolina, for analyses using the second type of mixed model analysis.

The following principal investigators participated in the study: P. M. Kaihlanen, MD, San Antonio, Tex.; William J. Mroczek, MD, Alexandria, Va,; Paul Sandall, MD, Albuquerque, N.M.; James A. Schoenberger, MD, Chicago; and Michael A. Weber, MD, Long Beach, Calif.

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2. Sokolow M, Werdegar D, Kain HK, Hinman AT. Relationship between level of blood pressure measured casually and by portable recorders and severity of complications in essential hypertension. Circulation 1966;34:279-98.

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